The area of a trapezoid with bases b1 and b2 and height h is what?

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Multiple Choice

The area of a trapezoid with bases b1 and b2 and height h is what?

Think about how the width of the trapezoid changes from bottom to top. One base is b1 at the bottom and the other base is b2 at the top, and the height between them is h. Because the width changes linearly as you move up, the average width across the height is (b1 + b2)/2. Multiply that average width by the height to get the area: area = h × (b1 + b2)/2. This also makes sense in a couple of checks: if the two bases are equal, it becomes a rectangle with area b1 × h. If one base were zero, you'd get the area of a triangle (1/2 × b1 × h), which aligns with the idea that a triangle is a trapezoid with one base reduced to zero. Using the full sum (b1 + b2) × h would double the true area because it treats the width as if it were constant at b1 + b2, not averaging across the height. So the correct expression is h times the average of the bases: (1/2)(b1 + b2) h.

Think about how the width of the trapezoid changes from bottom to top. One base is b1 at the bottom and the other base is b2 at the top, and the height between them is h. Because the width changes linearly as you move up, the average width across the height is (b1 + b2)/2. Multiply that average width by the height to get the area: area = h × (b1 + b2)/2.

This also makes sense in a couple of checks: if the two bases are equal, it becomes a rectangle with area b1 × h. If one base were zero, you'd get the area of a triangle (1/2 × b1 × h), which aligns with the idea that a triangle is a trapezoid with one base reduced to zero. Using the full sum (b1 + b2) × h would double the true area because it treats the width as if it were constant at b1 + b2, not averaging across the height. So the correct expression is h times the average of the bases: (1/2)(b1 + b2) h.

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